I haven't looked at all 900+ properties, but I've seen numerous examples where the property is most expensive booking via Hyatt, somewhat less booking through M&MS, and least expensive booking direct. You're paying for the WoH nights and points, and the perks offered through M&MS. You need to decide if those are worth the added cost ...
This is turning hotel loyalty on its head.
Normally, you're paying for the nights, points, and benefits by throwing the chain and its participating hotels incremental business. Room rates shouldn't be higher, though. For its non-MMS hotels, Hyatt even has a BRG (which isn't just for show; I still get claims accepted every now and then).